Losing weight isn't a one and done thing. It's something you'll have to try and maintain for the rest of your life until you decide it's not worth it.
I recommend that you take the weight loss journey (which is more of a change in lifestyle or a lifelong journey) slowly, even if it takes a year or two or longer to reach a reasonable target weight. If you think about it, a year or two really doesn't mean anything when it comes to losing weight. People stay the same weight or gain weight for years and years. Please don't pressure yourself with a time limit as EDs with extreme food noise can make you go insane.
Losing weight is mostly about CICO (calories in, calories out). You should be taking in less calories than the amount you burn to lose weight over time.
First, put your stats (height, weight, age, and sex) in a BMR calculator. It'll give you a general estimate of your BMR, or how many calories your body burns a day just by being alive. This number isn't 100% exact but it's accurate enough for most people. When you weigh yourself for the first time, I recommend you do it in the morning, naked, after you pee/poop so that the food/water weight doesn't affect the result too much.
A 25-year-old 5'5 female that weighs 130 lbs has a BMR of ~1350. That's how many calories they burn without any extra movement.
Your TDEE includes the number of extra calories you burn by exercise (normal daily movement or workouts) on top of your BMR. If the person in the example is really sedentary, then they might burn ~1,600 calories a day. With exercise, they could reasonably bump that up to ~1,800-1,900.
The lower the weight you start off with, the lower your calorie deficit can realistically be. But I would recommend trying not to go over a 500 calorie deficit. 1000 calorie deficits are on the extreme side and are only viable for a short period of time if you're morbidly obese. Honestly, just eating a little under maintenance and adding exercise like daily walks will be enough to slowly lose weight.
The weight you lose will be both fat and muscle as losing at least some muscle is inevitable if you're not hitting weights or doing any sort of body resistance workouts. Eventually you might hit a point where you go "why do I still look fat (skinnyfat)" when you're at a healthy weight. If this isn't the body dysmorphia talking, then it's because you need to build some muscle (no, it won't make you look like a bodybuilder and will actually make you look skinnier/leaner) to achieve more of the look you're looking for.
You can't spot reduce so don't obssess over the "problem parts" that look like they're not getting smaller. As you lose weight, eventually all of you will get smaller, just at different speeds. The parts you're concerned about are usually the ones that are last to show a difference. Like for someone with thick upper arms, it could take a long, long, long time for theirs to somewhat shrink. But progress takes patience.
I guess another tip would be to not obssess over the scale. Womens' weights fluctuate way more because of water weight and you'll only stress yourself out if you're weighing yourself daily/weekly and taking those numbers at face value. You could be 5 pounds heavier just from your period coming up. You should really be looking for a downward trend in weight over months of data.
This should all be done as healthily as you can though. EDs are really, really horrible and can consume your life. If you can, please work with a dietician (and psychiatrist) if it feels overwhelming.